An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a £1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip.
Here are the summary statistics for his data:
-Assuming the distribution of commute times is not strongly skewed in either sample, in evaluating the relationship between bike type and commute time, would a theory-based approach be valid?

Question

An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a £1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip.
Here are the summary statistics for his data: 
-Assuming the distribution of commute times is not strongly skewed in either sample, in evaluating the relationship between bike type and commute time, would a theory-based approach be valid?

Quizplus · Accepted Answer

A theory-based approach is valid if the sample sizes are sufficiently large, typically greater than 20. Here, both sample sizes (26 and 30) are larger than 20, making the theory-based approach appropriate.

An Article That Appeared in the British Medical Journal (2010)